Reconstruction of the Dirac Operator From Nodal Data

Abstract

Inverse nodal problems consist in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, we deal with the inverse nodal problem of reconstructing the Dirac operator on a finite interval. We prove that a dense subset of nodal points uniquely determine the parameters of the boundary conditions, the mass of a particle and the potential function of the Dirac system. We also provide a constructive procedure for the solution of the inverse nodal problem.